Summary: Pseudodifferential operators (PsDOs) on manifolds (definition, properties). Boundedness of PsDOs in anisotropic Sobolev spaces with weight. Factorization of matrix elliptic symbols and Fredholm properties of PsDOs. Asymptotics of solutions to elliptic systems of pseudodifferential equations. Application to some problems in elasticity.

B.-Wolfgang Schulze (University of Potsdam, Germany)

THE PSEUDODIFFERENTIAL CALCULUS FOR SINGULAR AND DEGENERATE OPERATORS

Summary: The lectures present the basic methods of PsDOs for solving elliptic and parabolic problems on configurations with singularities (conical, edge, corners, cuspidal etc.). Essential tools are the Mellin transform, meromorphic operator-valued symbols and weighted wedge Sobolev spaces with asymptotics. The calculus is aimed at constructing parametrices or inverses with the calculus and to illustrate the connection to concrete models in applied sciences.

This course is suitable for advanced graduate
students or recent Ph.D.'s. The participants will also have an opportunity to give 20-minute
talks on their own work at a mini-symposium which will take place during the Advanced Course.
Lectures and abstracts of the talks will be published and distributed among the lecturers and
participants after Advanced Course. The registration fee for participants is 400 USD which
includes all local expenses during the Advanced Course.
A restricted number of participants will be awarded grants.